Question: What do the following two equations represent? $5x+4y = 4$ $-8x+10y = 5$
Solution: Putting the first equation in $y = mx + b$ form gives: $5x+4y = 4$ $4y = -5x+4$ $y = -\dfrac{5}{4}x + 1$ Putting the second equation in $y = mx + b$ form gives: $-8x+10y = 5$ $10y = 8x+5$ $y = \dfrac{4}{5}x + \dfrac{1}{2}$ The slopes are negative inverses of each other, so the lines are perpendicular.